Some generalizations of the well-known Cauchy-Schwarz inequality and the analogous Cauchy-Bunyakovsky inequality involving four free parameters are given for both discrete and continuous cases. Several particular cases of interest are also analyzed. Some of the applications of our main results include (for example) the Wagner inequality.

We prove two new reverse Cauchy–Schwarz inequalities of additive and multiplicative types in a space equipped with a positive sesquilinear form with values in a C *-algebra. We apply our results to get some norm and integral inequalities. As a consequence, we improve a celebrated reverse Cauchy–Schwarz inequality due to G. Pólya and G. Szegö.

In this paper we take a refreshing look at a Cauchy–Schwarz type inner product inequalities. We also provide a Cauchy–Schwarz based proof and a refinement of Buzano’s inequality in inner product spaces. Some elementary applications such as trace inequalities for unitary matrices and discrete or integral inequalities are given. 2013 Elsevier Inc. All rights reserved.

An inequality is derived for the correlation of two univariate functions operating on symmetric bivariate normal random variables. The inequality is a simple consequence of the Cauchy-Schwarz inequality.

In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behavio...

In the course of realizing certain triangle centers as points that minimize certain quantities, C. Kimberling and P. Moses, in Math. Mag. 85 (2012) 221–227, discovered an inequality in three variables that generalizes the Cauchy-Schwarz inequality, and made a conjecture regarding a generalization of that inequality to an arbitrary number of variables. In this paper, we give a proof of a stronge...